Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1) consider,   α = 0.2 and σ = 0.7. The first factor is...

Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1)

consider,   α = 0.2 and σ = 0.7.

The first factor is currently used in the amount x₁ = 9, and the second factor is used in the amount x₂ = 3.  

a) When (x₁,x₂) = (9,3), how much output is being produced?

Output:    

b) When (x₁,x₂) = (9,3), what is the marginal product of factor 1?

Marginal product:   

c) When (x₁,x₂) = (9,3), what is the average product of factor 1?

Average product:    

d) When (x₁,x₂) = (9,3), what is the rate of technical substitution (a positive number)?

Rate of technical substitution:    

e) When (x₁,x₂) = (9,3), what is the elasticity of substitution (a positive number)?

Elasticity of substitution: